Method and system for analyzing large signal stability boundary of dc microgrid based on equivalent remodelling circuit

Abstract

The application provides a DC micro-grid large signal stability boundary analysis method and system based on an equivalent remodeling circuit, comprising the following steps: S1: constructing a controller equivalent circuit based on a DC micro-grid control strategy; wherein the controller equivalent circuit comprises an inertia loop equivalent circuit, a voltage loop equivalent circuit and a current loop equivalent circuit; S2: constructing an equivalent circuit model of the DC micro-grid based on the constructed controller equivalent circuit; constructing a global mixed potential function of the system based on the constructed system equivalent circuit model; and S3: performing DC micro-grid large signal stability analysis based on the constructed global mixed potential function.

Description

Technical Field

[0001] This invention relates to the field of stability analysis technology for power electronic DC microgrids, specifically to a method and system for large-signal stability boundary analysis of DC microgrids based on equivalent remodeling circuits, applicable to the quantitative evaluation of system stability boundaries and optimization design of control parameters under large disturbance conditions. Background Technology

[0002] The large-scale application of renewable energy is of great significance for promoting environmental sustainability and energy structure transformation. DC microgrids, with their advantages of efficient energy conversion and flexible integration of distributed energy sources, have become an effective carrier for realizing the localized consumption of renewable energy. However, many power electronic converters in the system exhibit strong coupling and nonlinear dynamic characteristics when facing frequent load switching and energy fluctuations. Traditional small-signal stability analysis methods fail when the system encounters large disturbances, such as large step load changes, because the operating point deviates significantly from the equilibrium position. In such cases, large-signal stability assessment is crucial for ensuring the reliable operation of the system.

[0003] Hybrid potential theory, by constructing hybrid potential functions based on the characteristics of circuit elements to verify Lyapunov stability, provides a clear criterion for the large-signal stability of systems and has become an important analytical tool in this field. However, this theory has an essential limitation: its hybrid potential functions can only be constructed based on physical circuit elements such as inductor current and capacitor voltage, while the state variables in the controller, lacking circuit-like representation, are difficult to incorporate into the hybrid potential function analysis framework. This makes it impossible to effectively quantify the influence mechanism of control parameters on system stability.

[0004] To circumvent this problem, existing research typically simplifies power electronic converters as ideal current sources and constructs a hybrid potential function containing only a subset of control parameters. This approach leads to two fundamental drawbacks: first, it fails to fully reflect the effects of key control variables such as proportional-integral coefficients and virtual inertia parameters in the controller; second, it makes it difficult to systematically analyze the stability boundary under the combined effects of all control parameters. When microgrids face large load disturbances in factory or commercial building scenarios, this simplified analysis method will struggle to guide the robust design of control parameters.

[0005] To address the aforementioned challenges, this invention proposes a method and system for large-signal stability analysis of DC microgrids based on an equivalent remodeled circuit. It innovatively remodels the controller's dynamic model into an RLC equivalent circuit, reconstructing the main circuit physical components and controller parameters within a unified circuit framework. This constructs a global hybrid potential function containing complete control parameters, enabling accurate characterization of the system's large-signal stability boundary. This method can guide controller parameter design and significantly improve the microgrid's resilience to large disturbances.

[0006] Existing literature, such as Wang Zhixun, Lin Xiangning, Ding Suyang, et al. AC / DC hybrid wind power generation system adapted to island independent microgrids and its optimal dispatch strategy [J]. Proceedings of the CSEE, 2018, 38(16): 4692-4704, 4974, discloses that independent island hybrid microgrids (IIHMs) can effectively solve the island power supply problem, but the fluctuation of renewable energy output exacerbates the power imbalance of AC / DC sub-microgrids, resulting in significant power loss during transmission and conversion. Therefore, this paper designs a hybrid brushless doubly-fed wind turbine generator (HBDFIG), which can directly distribute power to AC and DC sub-microgrids at a certain ratio on the generation side by actively adjusting the generator speed and controlling the winding current frequency. Based on this, with the premise of ensuring full power supply to the load and the goal of minimizing the consumption of power generation fuel in the island, an optimized generation dispatch strategy for IIHM containing HBDFIG is proposed. The numerical results show that HBDFIG and its optimized generation dispatch strategy can reduce power transmission and transformation losses within the microgrid, improve power supply efficiency, extend the conventional fuel replenishment cycle, and reduce the overall operating cost of island microgrids. This literature studies the power mutual assistance strategy for islanded AC / DC hybrid microgrids, proposing a bidirectional support method based on virtual inertia control. It coordinates the steady-state power allocation of AC frequency and DC voltage through interconnected converters and designs a hierarchical control strategy to optimize the power mutual assistance mode. However, the control strategy in this literature focuses on steady-state power autonomy and transient inertia support, without addressing the modeling of inertia mutual assistance between subgrids, nor quantifying the inertia sharing mechanism at the system level. In contrast, this invention proposes an equivalent circuit model for peer-to-peer inertia mutual assistance in hybrid AC / DC microgrids based on an equivalent remodeled circuit. This model constructs a global equivalent circuit by equating the subgrid inertia characteristics to a Thevenin circuit and combining it with the control loop of the bidirectional power converter, intuitively revealing the inertia sharing mechanism between subgrids. Compared with the literature, this invention not only breaks through the limitations of single subnet modeling, but also realizes the quantitative analysis of inertia through circuit model, simplifies the mathematical derivation of complex systems, and provides a more efficient theoretical tool for the dynamic characteristic analysis and control design of multi-subnet inertia mutual assistance.

[0007] Existing literature, Tian Hao, Huang Wentao, Yu Moduo, et al. Adaptive bidirectional droop control strategy for AC / DC hybrid independent microgrid interconnection converter [J]. Proceedings of the CSEE, 2022, 42(19):7063-7074, discloses an adaptive bidirectional droop control strategy for an independent hybrid microgrid interconnection converter to solve the problem of the interconnection converter's inability to meet optimal control under multiple operating conditions. Based on the normalization method, the AC frequency and DC voltage are uniformly controlled. The priority of AC microgrid frequency control and DC microgrid voltage control in bidirectional droop control is determined by adaptive weighting coefficients, enabling the interconnection converter to prioritize support for the side with larger AC frequency or DC voltage deviation, ensuring that the frequency and voltage of both systems are maintained within the optimal range. The dead zone of the action is designed to optimize the start-up conditions and reduce unnecessary actions of the interconnection converter. A small-signal model of the system is established, and the stability of the proposed control strategy is verified through root locus analysis. Finally, a simulation model of an AC / DC hybrid microgrid was established in PSCAD / EMTDC, and an RT-LAB experimental platform was built. Simulation and experimental results show that the proposed strategy is reliable and effective, improving the stability of the active power component of the AC / DC hybrid microgrid under different scenarios. This previous paper studied the power mutual assistance strategy for islanded AC / DC hybrid microgrids, proposing a bidirectional support method based on virtual inertia control. This method coordinates the steady-state power distribution of AC frequency and DC voltage through interconnected converters and designs a hierarchical control strategy to optimize the power mutual assistance mode. However, this method mainly focuses on the inertia modeling and control parameter design of a single subgrid (such as the AC or DC side), lacking a global quantitative analysis of the inertia mutual assistance mechanism between AC and DC subgrids, and failing to unify the subgrid inertia characteristics into an intuitively analytical circuit model. In contrast, this invention proposes a global equivalent circuit model for equal inertia mutual assistance in hybrid AC / DC microgrids based on an equivalent remodeling circuit. This model constructs a global equivalent circuit containing the inertia transfer path by equating the inertia characteristics of each subnet to Thevenin circuits and combining it with the control logic of a bidirectional power converter, thus achieving an intuitive quantitative analysis of the total system inertia. Compared with the previous paper, this invention not only overcomes the limitations of single subnet modeling but also simplifies the mathematical derivation of complex systems through circuit modeling, providing a more efficient theoretical tool for the dynamic characteristic analysis and control design of multi-subnet inertia mutual support. Summary of the Invention

[0008] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for large-signal stability boundary analysis of DC microgrids based on equivalent remodeling circuits.

[0009] The present invention provides a method for large-signal stability boundary analysis of DC microgrids based on equivalent remodeling circuits, comprising: Step S1: Construct the equivalent circuit of the controller based on the DC microgrid control strategy; wherein, the equivalent circuit of the controller includes: an inertia loop equivalent circuit, a voltage loop equivalent circuit, and a current loop equivalent circuit; Step S2: Construct an equivalent circuit model of the DC microgrid based on the constructed controller equivalent circuit; construct the global hybrid potential function of the system based on the constructed system equivalent circuit model; Step S3: Perform large-signal stability analysis of DC microgrid based on the constructed global hybrid potential function.

[0010] Preferably, the inertia loop equivalent circuit includes: (1) Where, Δ v bus This refers to the DC bus voltage deviation; Δ P s For power fluctuations; F HP and T RH The time constant in the transfer function of the thermal turbine in a synchronous generator; H, D and k d and are the inertia, damping, and droop coefficient of the synchronous generator, respectively; s For the Laplace operator.

[0011] Preferably, the voltage loop equivalent circuit includes: (2) in, v bus_ref This is the reference value for the inner loop voltage; v bus This is the DC bus voltage; k vp This refers to the proportional coefficient in the voltage loop PI controller; k vi The integral coefficient; s For the Laplace operator; i L_ref This is the reference value for the current loop; for( v bus_ref - v bus ).

[0012] Preferably, the current loop equivalent circuit includes: (3) in, i L_ref This is the reference value for the current loop; i LsInductor L s The measured value of the current. k ip This refers to the proportional coefficient in the current loop PI controller; k ii The integral coefficient; for( i L_ref - i Ls ); d This represents the duty cycle of the DC microgrid converter.

[0013] Preferably, step S2 includes: Step S2.1: Based on the controller equivalent circuit, integrate the main circuit with the controller equivalent circuit to form a system equivalent circuit model; the main circuit includes: physical inductance, capacitance, resistance, and load; Step S2.2: Based on the system's equivalent circuit model, construct the system's global mixed potential function; (4) in, R d 、R Ld This refers to the resistance in the equivalent circuit of the inertia loop. i Ld Inductance in the equivalent circuit of the inertia loop L d The current, v Cd The capacitance C in the equivalent circuit of the inertia loop d The voltage; R s The resistance of the converter's equivalent circuit. i L Inductance in the equivalent circuit of the converter L s The current, P s This represents the power value of a constant power load. v bus Capacitor of the converter equivalent circuit C s voltage, R vkp The resistance is the equivalent circuit resistance of the voltage loop. i vkp Inductance in the voltage loop equivalent circuit L vki The current, v bus_max for v bus The maximum value, vbus_ref for v bus Reference value, i L_ref This represents the current of the controlled current source in the current loop equivalent circuit. d The duty cycle of the DC microgrid converter is represented as a resistance in the current loop equivalent circuit. R ikp and capacitor C iki The sum of voltages, v iki For capacitor C iki The voltage; The state variable column vector of a DC microgrid is defined as follows: ,in, This is a column vector consisting of all inductor currents in the controller's equivalent circuit and the actual physical circuit. This is a column vector consisting of all capacitor voltages in the controller's equivalent circuit and the actual physical circuit; its dynamics are described by the mixed potential function differential equation: (5) in, This is a diagonal matrix containing all inductors L and capacitors C; through coordinate transformation: (6) in, (7) Derive the sufficient condition for ensuring the stability of large signals in a DC microgrid: (8) Here, μ 1 is the smallest eigenvalue of the matrix. A ii ( i ) is the potential function P ( x The second-order partial derivative matrix with respect to the inductor current, μ 2 is a matrix C 1 / 2 B vv ( v ) C 1 / 2 The smallest eigenvalue, where, B vv ( v ) is the potential function P ( xThe second-order partial derivative matrix with respect to the capacitor voltage; for the system hybrid function constructed by equation (4), its μ 1 and μ The specific expression for 2 is: (9) in, R Ld This refers to the resistance in the equivalent circuit of the inertia loop. R s The resistance of the converter's equivalent circuit. R ikp This is the resistance in the equivalent circuit of the current loop. L s The inductance in the equivalent circuit of the converter. L d C is the inductance in the equivalent circuit of the inertia loop; d C is the capacitance in the equivalent circuit of the inertia loop. d This refers to the capacitance in the equivalent circuit of the inertia loop. R d This refers to the resistance in the equivalent circuit of the inertia loop. P s This represents the power value of a constant power load. C s The capacitance of the converter's equivalent circuit. v bus Capacitor of the converter equivalent circuit C s voltage, R vkp The resistor is the resistor in the equivalent circuit of the medium voltage loop.

[0014] Preferably, step S3 includes: based on stability criteria μ 1+ μ 2>0 Quantitatively assess the impact of parameters.

[0015] Preferably, the method further includes: increasing the virtual inertia coefficient. H or damping coefficient D Or reduce the filter inductance L d All of them were improved μ 1+ μ The 2-value enhances stability and expands the range of load disturbances that the DC microgrid can withstand.

[0016] The present invention provides a large-signal stability boundary analysis system for DC microgrids based on an equivalent remodeling circuit, comprising: Module M1: Constructs an equivalent circuit for the controller based on a DC microgrid control strategy; wherein, the equivalent circuit for the controller includes: an equivalent circuit for the inertia loop, an equivalent circuit for the voltage loop, and an equivalent circuit for the current loop; Module M2: Constructs an equivalent circuit model of the DC microgrid based on the constructed controller equivalent circuit; constructs the global hybrid potential function of the system based on the constructed system equivalent circuit model; Module M3: Performs large-signal stability analysis of DC microgrids based on the constructed global hybrid potential function.

[0017] Preferably, the inertia loop equivalent circuit includes: (1) Where, Δ v bus This refers to the DC bus voltage deviation; Δ P s For power fluctuations; F HP and T RH The time constant in the transfer function of the thermal turbine in a synchronous generator; H, D and k d and are the inertia, damping, and droop coefficient of the synchronous generator, respectively; s For the Laplace operator; The voltage loop equivalent circuit includes: (2) in, v bus_ref This is the reference value for the inner loop voltage; v bus This is the DC bus voltage; k vp This refers to the proportional coefficient in the voltage loop PI controller; k vi The integral coefficient; s For the Laplace operator; i L_ref This is the reference value for the current loop; for( v bus_ref - v bus ); The current loop equivalent circuit includes: (3) in, i L_ref This is the reference value for the current loop; i Ls Inductor L s The measured value of the current. k ip This refers to the proportional coefficient in the current loop PI controller; k ii The integral coefficient; for( i L_ref - i Ls ); d This represents the duty cycle of the DC microgrid converter.

[0018] Preferably, the module M2 includes: Module M2.1: Based on the controller equivalent circuit, the main circuit and the controller equivalent circuit are integrated to form a system equivalent circuit model; the main circuit includes: physical inductance, capacitance, resistance, and load; Module M2.2: Based on the system's equivalent circuit model, construct the system's global mixed potential function; (4) in, R d 、R Ld This refers to the resistance in the equivalent circuit of the inertia loop. i Ld Inductance in the equivalent circuit of the inertia loop L d The current, v Cd The capacitance C in the equivalent circuit of the inertia loop d The voltage; R s The resistance of the converter's equivalent circuit. i L Inductance in the equivalent circuit of the converter L s The current, P s This represents the power value of a constant power load. v bus Capacitor of the converter equivalent circuit C s voltage, R vkp The resistance is the equivalent circuit resistance of the voltage loop. i vkp Inductance in the voltage loop equivalent circuit L vki The current, v bus_max for v bus The maximum value, v bus_ref for v bus Reference value, i L_ref This represents the current of the controlled current source in the current loop equivalent circuit. dThe duty cycle of the DC microgrid converter is represented as a resistance in the current loop equivalent circuit. R ikp and capacitor C iki The sum of voltages, v iki For capacitor C iki The voltage; The state variable column vector of a DC microgrid is defined as follows: ,in, This is a column vector consisting of all inductor currents in the controller's equivalent circuit and the actual physical circuit. This is a column vector consisting of all capacitor voltages in the controller's equivalent circuit and the actual physical circuit; its dynamics are described by the mixed potential function differential equation: (5) in, This is a diagonal matrix containing all inductors L and capacitors C; through coordinate transformation: (6) in, (7) Derive the sufficient condition for ensuring the stability of large signals in a DC microgrid: (8) Here, μ 1 is the smallest eigenvalue of the matrix. A ii ( i ) is the potential function P ( x The second-order partial derivative matrix with respect to the inductor current, μ 2 is a matrix C 1 / 2 B vv ( v ) C 1 / 2 The smallest eigenvalue, where, B vv ( v ) is the potential function P ( x The second-order partial derivative matrix with respect to the capacitor voltage; for the system hybrid function constructed by equation (4), its μ 1 and μ The specific expression for 2 is: (9) in, RLd This refers to the resistance in the equivalent circuit of the inertia loop. R s The resistance of the converter's equivalent circuit. R ikp This is the resistance in the equivalent circuit of the current loop. L s The inductance in the equivalent circuit of the converter. L d C is the inductance in the equivalent circuit of the inertia loop; d C is the capacitance in the equivalent circuit of the inertia loop. d This refers to the capacitance in the equivalent circuit of the inertia loop. R d This refers to the resistance in the equivalent circuit of the inertia loop. P s This represents the power value of a constant power load. C s The capacitance of the converter's equivalent circuit. v bus Capacitor of the converter equivalent circuit C s voltage, R vkp The resistance is the equivalent circuit resistance of the medium voltage loop. The module M3 includes: based on stability criteria μ 1+ μ 2>0 Quantitatively assess the impact of parameters.

[0019] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention reshapes the dynamic model of the controller into an RLC equivalent circuit, so that the control parameters, such as proportional-integral coefficients and virtual inertia parameters, can obtain a circuit representation form. 2. Based on the coupling characteristics of the physical components of the main circuit and the equivalent circuit of the controller, this invention establishes a global hybrid potential function containing complete system parameters, thereby achieving accurate characterization of the large-signal stability boundary of the DC microgrid. 3. Based on the characterized large-signal stability boundary, this invention provides controller parameter design criteria, which significantly improves the robustness of microgrids under large load disturbances in factory or commercial building scenarios. 4. This invention solves the key problem that traditional hybrid potential theory (MPT) cannot directly analyze the impact of controller state variables and their parameters, such as proportional-integral coefficients, inertia coefficients, and damping coefficients, on the large-signal stability of the system by reshaping the dynamic model of the controller, especially virtual inertia control and dual-loop PI control, into equivalent RLC circuit elements. This provides a circuit-level foundation for comprehensively evaluating the contribution of control strategies to system stability. 5. This invention constructs a globally unified circuit model that includes the main circuit and the equivalent circuit of the reshaped controller, and establishes a generalized hybrid potential function based on it. For the first time, it realizes the cooperative large-signal stability analysis of the circuit physical parameters and controller parameters, and derives a universal stability criterion μ1+μ2>0. It accurately describes the stability boundary of the system when it encounters large disturbances, such as large step load changes. It breaks through the limitation of traditional MPT being only applicable to physical circuit elements, and provides a unified and rigorous theoretical framework for system stability assessment. 6. The analysis method proposed in this invention can clearly quantify the specific impact of key parameters on the stability margin of the system, and clearly reveal that increasing the virtual inertia coefficient H, the damping coefficient D, and decreasing the filter inductance Ld can effectively extend the stable operating range of the system and improve its ability to resist large disturbances. Attached Figure Description

[0020] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figures 1a to 1c This is the converter topology and its control block diagram.

[0021] Figure 2 This is the converter topology and its control block diagram.

[0022] Figure 3 This diagram illustrates the impact of virtual inertia coefficient and damping coefficient on the stability of large signals.

[0023] Figure 4 This is a schematic diagram illustrating the impact of filter inductance and maximum load power on signal stability.

[0024] Figures 5a to 5b This is a schematic diagram showing the simulation results of the system parameters on the stability of large signals. Detailed Implementation

[0025] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0026] Example 1 This invention provides a method and system for large-signal stability analysis of DC microgrids based on equivalent remodeled circuits. Unlike traditional Mixed Potential Theory (MPT), which can only construct mixed potential functions based on physical circuit elements for stability analysis and struggles to analyze the impact of non-circuitous state variables in the controller on stability, this invention equivalently remodels the dynamic characteristics of the controller into an RLC circuit, constructing a unified system model including the main circuit and the equivalent control circuit. Then, it applies generalized MPT to perform unified large-signal stability analysis and boundary characterization of the system containing all control parameters.

[0027] The method for analyzing the large-signal stability of DC microgrids based on equivalent remodeling circuits includes: Step S1: Construct the equivalent circuit of the controller based on the DC microgrid control strategy; wherein, the equivalent circuit of the controller includes: an inertia loop equivalent circuit, a voltage loop equivalent circuit, and a current loop equivalent circuit; Specifically, mixed potential theory (MPT) verifies Lyapunov stability by constructing mixed potential functions based on the characteristics of circuit elements, providing a clear criterion for the large-signal stability of systems and becoming an important analytical tool in this field. However, this theory has an inherent limitation: its mixed potential function can only be constructed based on physical circuit elements such as inductor current and capacitor voltage, while the state variables in the controller, lacking circuit representation, are difficult to incorporate into the mixed potential function analysis framework. To address this issue, this invention reshapes the dynamic characteristics of the controller into an equivalent RLC circuit, enabling MPT to be applied to analyze the impact of state variables in the controller on large-signal stability.

[0028] A schematic diagram of the renewable energy interface converter topology is shown below. Figure 1a As shown, renewable energy sources in a DC microgrid are typically connected to the DC bus via power electronic converters to supply power to the DC system. Since power electronic converters lack the inertia provided by synchronous generators, a virtual inertia control strategy is usually introduced into the converter to enhance the system's inertia. The virtual inertia control block diagram is shown below. Figure 1b As shown, virtual inertia control includes key parameters such as thermal turbine coefficient, equivalent droop coefficient, inertia coefficient, and damping coefficient. The overall control block diagram of the converter is shown below. Figure 1c As shown, the outermost loop is a virtual inertia control, and the inner loop is a dual-loop control structure of voltage and current. The limitation of traditional MPTs lies in the fact that their hybrid potential function can only be constructed based on physical state variables such as inductor current and capacitor voltage, while the state variables in the controller, such as the proportional coefficient, inertia, and virtual coefficient of PI control, cannot be directly expressed as a potential function. To overcome this limitation, this invention reshapes the control strategy as follows: Figure 2 The equivalent circuit shown.

[0029] The equivalent circuit of the inertia loop is derived as follows: Based on... Figure 1b The virtual inertia control block diagram shown can be used to obtain the DC bus voltage deviation Δ. v bus To power fluctuation Δ P s The transfer function is as follows: (1) Wherein: F HP and T RH The time constant in the transfer function of the thermal turbine in a synchronous generator; H, D and k d and are the inertia, damping, and droop coefficient of the synchronous generator, respectively.

[0030] If we take Δ in equation (1) v bus and Δ P s If we consider them as voltage drop and current respectively, then Δ v bus With Δ P s The ratio can be equivalent to Figure 2 The equivalent circuit of the inertia loop in the diagram. For ease of explanation, let... L d = k d T RH / (1 F HP ), R Ld = k d / (1 F HP ), R d = D / ( Dk d + F HP ), C d =1 / 2 H Let the above expression be denoted as - Y d and combined Figure 1c The reference value of the inner loop voltage can be obtained from the overall system control block diagram shown. v bus_ref as follows (2) In the formula: v bus_max This represents the maximum DC bus voltage.

[0031] The equivalent circuit of the voltage loop is derived as follows: Based on Figure 1c The voltage loop control block diagram shown can be used to obtain the voltage loop dynamic characteristics shown in equation (3), where, v err = v bus_ref - v bus This indicates the deviation between the bus voltage and its reference value. i L_ref This is the reference value for the current loop. Assume the proportional gain in the voltage loop PI controller is... k vp and integral coefficient k vi Resistors R vp and inductor L vki The value, then v err k vp and k vi v err / s These can be considered as resistive current and inductive current, respectively. Therefore, equation (3) can be further expressed as Figure 2 The voltage loop equivalent circuit in the diagram.

[0032] (3) The equivalent circuit of the current loop is derived as follows: Based on Figure 1c The current loop control block diagram shown yields the current loop dynamic characteristics shown in equation (4). If the duty cycle is... d When considered as an equivalent voltage, this voltage can be understood as a current. i errx The total voltage drop occurs through the resistor branch and the capacitor branch. Assume the proportional gain in the current loop PI controller... k ip The reciprocal of the integral coefficient 1 / k ii Resistors R ip and inductor C ipx The value, then i err k ip and k ii i err / sThese can be considered as resistor voltage and inductor voltage, respectively. Based on this equivalent relationship, the dynamic process of the current loop can be reconstructed as follows: Figure 2 The current-equivalent circuit in the middle.

[0033] (4) Step S2: Construct the system equivalent circuit model based on the constructed controller equivalent circuit; construct the global mixed potential function of the system based on the constructed system equivalent circuit model; Specifically, a global model is constructed based on the reconstructed equivalent circuit, and the MPT is applied to derive the large-signal stability criterion for DC microgrids.

[0034] Based on the reshaping of the controller's equivalent circuit, the main circuit, including physical inductors, capacitors, resistors, and loads, is integrated with the aforementioned control equivalent circuit to form a unified equivalent circuit model for large-signal stability analysis. Based on this unified model, the system's global mixed potential function is constructed using the reshaped equivalent circuit. P ( i , v This potential function combines the energy characteristics of the physical circuit elements and the reshaped control equivalent circuit elements, and its formal definition is as follows: (5) The system's state variable column vector is defined as follows: Its dynamics are described by the differential equation of the mixed potential function: (6) in

[0035] This is a diagonal matrix containing all inductors L and capacitors C. (This is achieved through coordinate transformation.) (7) in

[0036] Derive the sufficient condition for ensuring the stability of large signals in the system: (8) Here μ 1 is the smallest eigenvalue of the matrix. A ii ( i ) is the potential function P ( x (Second-order partial derivative matrix with respect to inductor current) μ 2 is a matrix C 1 / 2 B vv( v ) C 1 / 2 The smallest eigenvalue ( B vv ( v ) is the potential function P ( x (The second-order partial derivative matrix with respect to the capacitor voltage). For the hybrid function of the system constructed by equation (5), its μ 1 and μ The specific expression for 2 is: (9) Step S3: Perform large-signal stability analysis of DC microgrid based on the constructed global hybrid potential function.

[0037] Specifically, based on stability criteria μ 1+ μ The 2>0 quantification evaluates the impact of parameters and accurately characterizes the stability boundary of the system's large signal.

[0038] Based on stability criteria μ 1+ μ A value greater than 2 allows for systematic analysis of the impact of parameters on the large-signal stability of DC microgrids and precise characterization of stability boundaries. Key conclusions include: increasing the virtual inertia coefficient. H or damping coefficient D Or reduce the filter inductance L d All of them were improved μ 1+ μ A value of 2 enhances stability and expands the range of load disturbances the system can withstand (i.e., the stability boundary). For example, the damping coefficient... D x Increasing the value from 0.35 to 0.7 allows for a maximum allowable load power before system instability. P L An improvement of 14%. This quantitative relationship provides insights for designing robust controller parameters, such as optimization. H , D , k vp , k ip This provides a direct basis for ensuring safe and stable operation under large disturbances (such as load jumps).

[0039] The present invention also provides a large-signal stability boundary analysis system for DC microgrids based on equivalent remodeling circuits. The large-signal stability boundary analysis system for DC microgrids based on equivalent remodeling circuits can be implemented by executing the process steps of the large-signal stability boundary analysis method for DC microgrids based on equivalent remodeling circuits. That is, those skilled in the art can understand the large-signal stability boundary analysis method for DC microgrids based on equivalent remodeling circuits as a preferred embodiment of the large-signal stability boundary analysis system for DC microgrids based on equivalent remodeling circuits.

[0040] Example 2 Example 2 is a preferred example of Example 1. To verify the effectiveness of the proposed generalized mixed potential function theory (GMPT) in large-signal stability analysis, a DC microgrid system model was built on the MATLAB / Simulink platform, and the system parameters were strictly configured according to Table 1.

[0041] Table 1 Overall System Parameters

[0042] The stability criterion can be calculated based on Table 1 and Formula (9). μ 1+ μ 2. Figure 3 Showing different inertia coefficients H and damping coefficient D Down μ 1+ μ The value of 2 is used for analysis. H and D Impact on the stability of large signals in DC microgrids. Figure 4 Demonstrates the unfiltered inductor L s and constant power load P L Down μ 1+ μ The value of 2 is used for analysis. L s and P L Impact on the stability of large signals in DC microgrids.

[0043] To fully verify the correctness of the large-signal stability boundary obtained in this paper based on the equivalent remodeling circuit, two sets of comparative operating conditions are set up: Operating condition one involves gradually reducing the system inertia coefficient. H or damping coefficient D Until the system operating point crosses the stability boundary; under operating condition two, the load power is increased synchronously. P L With filter inductor L d Until the system enters the unstable region.

[0044] Reducing inertia or damping beyond the stability boundary can lead to bus voltage instability, such as... Figure 5a As shown, when H From 0.0035 to 0.0015 (a decrease of 57%) or D When the DC bus voltage drops from 0.35 to 0.15 (a decrease of 57%), v bus The value drops to 0, causing system instability. P L Or, the filter inductance increases beyond the stability boundary, causing bus voltage instability, such as... Figure 5b As shown, when P L Increase by 40% or L dx When the DC bus voltage increases from 3mH to 5mH, v bus When the value drops to 0, the system becomes unstable. The above results perfectly match the theoretical stability boundary predictions, demonstrating the correctness of the large-signal stability boundary obtained from the equivalent reshaped circuit.

[0045] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0046] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for large-signal stability boundary analysis of DC microgrids based on equivalent remodeling circuits, characterized in that, include: Step S1: Construct the equivalent circuit of the controller based on the DC microgrid control strategy; wherein, the equivalent circuit of the controller includes: an inertia loop equivalent circuit, a voltage loop equivalent circuit, and a current loop equivalent circuit; Step S2: Construct an equivalent circuit model of the DC microgrid based on the constructed controller equivalent circuit; construct the global hybrid potential function of the system based on the constructed system equivalent circuit model; Step S3: Perform large-signal stability analysis of DC microgrid based on the constructed global hybrid potential function.

2. The method for large-signal stability boundary analysis of DC microgrids based on equivalent remodeling circuits according to claim 1, characterized in that, The equivalent circuit of the inertia loop includes: （1） Where, Δ v bus This refers to the DC bus voltage deviation; Δ P s For power fluctuations; F HP and T RH The time constant in the transfer function of the thermal turbine in a synchronous generator; H, D and k d and are the inertia, damping, and droop coefficient of the synchronous generator, respectively; s For the Laplace operator.

3. The method for large-signal stability boundary analysis of DC microgrids based on equivalent remodeling circuits according to claim 1, characterized in that, The voltage loop equivalent circuit includes: （2） in, v bus_ref This is the reference value for the inner loop voltage; v bus This is the DC bus voltage; k vp This refers to the proportional coefficient in the voltage loop PI controller; k vi The integral coefficient; s For the Laplace operator; i L_ref This is the reference value for the current loop; for( v bus_ref - v bus ).

4. The method for large-signal stability boundary analysis of DC microgrids based on equivalent remodeling circuits according to claim 1, characterized in that, The current loop equivalent circuit includes: （3） in, i L_ref This is the reference value for the current loop; i Ls Inductor L s The measured value of the current. k ip This refers to the proportional coefficient in the current loop PI controller; k ii The integral coefficient; for( i L_ref - i Ls ); d This represents the duty cycle of the DC microgrid converter.

5. The method for large-signal stability boundary analysis of DC microgrids based on equivalent remodeling circuits according to claim 1, characterized in that, Step S2 includes: Step S2.1: Based on the controller equivalent circuit, integrate the main circuit with the controller equivalent circuit to form a system equivalent circuit model; the main circuit includes: physical inductance, capacitance, resistance, and load; Step S2.2: Based on the system's equivalent circuit model, construct the system's global mixed potential function; （4） in, R d 、R Ld This refers to the resistance in the equivalent circuit of the inertia loop. i Ld Inductance in the equivalent circuit of the inertia loop L d The current, v Cd The capacitance C in the equivalent circuit of the inertia loop d The voltage; R s The resistance of the converter's equivalent circuit. i L Inductance in the equivalent circuit of the converter L s The current, P s This represents the power value of a constant power load. v bus Capacitor of the converter equivalent circuit C s voltage, R vkp The resistance is the equivalent circuit resistance of the voltage loop. i vkp Inductance in the voltage loop equivalent circuit L vki The current, v bus_max for v bus The maximum value, v bus_ref for v bus Reference value, i L_ref This represents the current of the controlled current source in the current loop equivalent circuit. d The duty cycle of the DC microgrid converter is represented as a resistance in the current loop equivalent circuit. R ikp and capacitor C iki The sum of voltages, v iki For capacitor C iki The voltage; The state variable column vector of a DC microgrid is defined as follows: ,in, This is a column vector consisting of all inductor currents in the controller's equivalent circuit and the actual physical circuit. This is a column vector consisting of all capacitor voltages in the controller's equivalent circuit and the actual physical circuit; its dynamics are described by the mixed potential function differential equation: （5） in, This is a diagonal matrix containing all inductors L and capacitors C; through coordinate transformation: （6） in, （7） Derive the sufficient condition for ensuring the stability of large signals in a DC microgrid: （8） Here, μ 1 is the smallest eigenvalue of the matrix. A ii ( i ) is the potential function P ( x The second-order partial derivative matrix with respect to the inductor current, μ 2 is a matrix C 1 / 2 B vv ( v ) C 1 / 2 The smallest eigenvalue, where, B vv ( v ) is the potential function P ( x The second-order partial derivative matrix with respect to the capacitor voltage; for the system hybrid function constructed by equation (4), its μ 1 and μ The specific expression for 2 is: （9） in, R Ld This refers to the resistance in the equivalent circuit of the inertia loop. R s The resistance of the converter's equivalent circuit. R ikp This is the resistance in the equivalent circuit of the current loop. L s The inductance in the equivalent circuit of the converter. L d C is the inductance in the equivalent circuit of the inertia loop; d C is the capacitance in the equivalent circuit of the inertia loop. d This refers to the capacitance in the equivalent circuit of the inertia loop. R d This refers to the resistance in the equivalent circuit of the inertia loop. P s This represents the power value of a constant power load. C s The capacitance of the converter's equivalent circuit. v bus Capacitor of the converter equivalent circuit C s voltage, R vkp The resistor is the resistor in the equivalent circuit of the medium voltage loop.

6. The method for large-signal stability boundary analysis of DC microgrids based on equivalent remodeling circuits according to claim 5, characterized in that, Step S3 includes: based on stability criteria μ 1+ μ 2>0 Quantitatively assess the impact of parameters.

7. The method for large-signal stability boundary analysis of DC microgrids based on equivalent remodeling circuits according to claim 5, characterized in that, The method further includes: increasing the virtual inertia coefficient. H or damping coefficient D Or reduce the filter inductance L d All of them were improved μ 1+ μ The 2-value enhances stability and expands the range of load disturbances that the DC microgrid can withstand.

8. A large-signal stability boundary analysis system for DC microgrids based on equivalent remodeling circuits, characterized in that, include: Module M1: Constructs an equivalent circuit for the controller based on a DC microgrid control strategy; wherein, the equivalent circuit for the controller includes: an equivalent circuit for the inertia loop, an equivalent circuit for the voltage loop, and an equivalent circuit for the current loop; Module M2: Constructs an equivalent circuit model of the DC microgrid based on the constructed controller equivalent circuit; constructs the global hybrid potential function of the system based on the constructed system equivalent circuit model; Module M3: Performs large-signal stability analysis of DC microgrids based on the constructed global hybrid potential function.

9. The DC microgrid large-signal stability boundary analysis system based on equivalent reshaping circuit according to claim 8, characterized in that, The equivalent circuit of the inertia loop includes: （1） Where, Δ v bus This refers to the DC bus voltage deviation; Δ P s For power fluctuations; F HP and T RH The time constant in the transfer function of the thermal turbine in a synchronous generator; H, D and k d and are the inertia, damping, and droop coefficient of the synchronous generator, respectively; s For the Laplace operator; The voltage loop equivalent circuit includes: （2） in, v bus_ref This is the reference value for the inner loop voltage; v bus This is the DC bus voltage; k vp This refers to the proportional coefficient in the voltage loop PI controller; k vi The integral coefficient; s For the Laplace operator; i L_ref This is the reference value for the current loop; for( v bus_ref - v bus ); The current loop equivalent circuit includes: （3） in, i L_ref This is the reference value for the current loop; i Ls Inductor L s The measured value of the current. k ip This refers to the proportional coefficient in the current loop PI controller; k ii The integral coefficient; for( i L_ref - i Ls ); d This represents the duty cycle of the DC microgrid converter.

10. The DC microgrid large-signal stability boundary analysis system based on equivalent remodeling circuit according to claim 8, characterized in that, The module M2 includes: Module M2.1: Based on the controller equivalent circuit, the main circuit and the controller equivalent circuit are integrated to form a system equivalent circuit model; the main circuit includes: physical inductance, capacitance, resistance, and load; Module M2.2: Based on the system's equivalent circuit model, construct the system's global mixed potential function; （4） in, R d 、R Ld This refers to the resistance in the equivalent circuit of the inertia loop. i Ld Inductance in the equivalent circuit of the inertia loop L d The current, v Cd The capacitance C in the equivalent circuit of the inertia loop d The voltage; R s The resistance of the converter's equivalent circuit. i L Inductance in the equivalent circuit of the converter L s The current, P s This represents the power value of a constant power load. v bus Capacitor of the converter equivalent circuit C s voltage, R vkp The resistance is the equivalent circuit resistance of the voltage loop. i vkp Inductance in the voltage loop equivalent circuit L vki The current, v bus_max for v bus The maximum value, v bus_ref for v bus Reference value, i L_ref This represents the current of the controlled current source in the current loop equivalent circuit. d The duty cycle of the DC microgrid converter is represented as a resistance in the current loop equivalent circuit. R ikp and capacitor C iki The sum of voltages, v iki For capacitor C iki The voltage; The state variable column vector of a DC microgrid is defined as follows: ,in, This is a column vector consisting of all inductor currents in the controller's equivalent circuit and the actual physical circuit. This is a column vector consisting of all capacitor voltages in the controller's equivalent circuit and the actual physical circuit; its dynamics are described by the mixed potential function differential equation: （5） in, This is a diagonal matrix containing all inductors L and capacitors C; through coordinate transformation: （6） in, （7） Derive the sufficient condition for ensuring the stability of large signals in a DC microgrid: （8） Here, μ 1 is the smallest eigenvalue of the matrix. A ii ( i ) is the potential function P ( x The second-order partial derivative matrix with respect to the inductor current, μ 2 is a matrix C 1 / 2 B vv ( v ) C 1 / 2 The smallest eigenvalue, where, B vv ( v ) is the potential function P ( x The second-order partial derivative matrix with respect to the capacitor voltage; for the system hybrid function constructed by equation (4), its μ 1 and μ The specific expression for 2 is: （9） in, R Ld This refers to the resistance in the equivalent circuit of the inertia loop. R s The resistance of the converter's equivalent circuit. R ikp This is the resistance in the equivalent circuit of the current loop. L s The inductance in the equivalent circuit of the converter. L d C is the inductance in the equivalent circuit of the inertia loop; d C is the capacitance in the equivalent circuit of the inertia loop. d This refers to the capacitance in the equivalent circuit of the inertia loop. R d This refers to the resistance in the equivalent circuit of the inertia loop. P s This represents the power value of a constant power load. C s The capacitance of the converter's equivalent circuit. v bus Capacitor of the converter equivalent circuit C s voltage, R vkp The resistance is the equivalent circuit resistance of the medium voltage loop. The module M3 includes: based on stability criteria μ 1+ μ 2>0 Quantitatively assess the impact of parameters.

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